Question

Arktec Manufacturing is considering two options for making Product A. The cost structures for the two options are shown below:

	Fixed Cost (Per Year)	Variable Cost (Per Unit)
Option 1	$500,000	$2 per unit
Option 2	$100,000	$10 per unit

Furthermore, ArkTec has identified two possible demand scenarios for Product A.

Demand (Units Per Year)	Probability
50,000	40%
100,000	60%

At what volume level do the two capacity options have identical costs?

What is the expected value in cost for Option 1 only?

Suppose Product A sells for $12. What is the break-even point for Option 2 only?

Answer 1

(1) If the equivalent quantity be Q, then

$500,000 + $2 x Q = $100,000 + $10 x Q

$8 x Q = $400,000

Q = 50,000 units

(2)

When Q = 50,000 units, Total cost ($) = 500,000 + (2 x 50,000) = 500,000 + 100,000 = 600,000

When Q = 100,000 units, Total cost ($) = 500,000 + (2 x 100,000) = 500,000 + 200,000 = 700,000

Expected Total cost ($) = 40% x 600,000 + 60% x 700,000 = 240,000 + 420,000 = 660,000

(3)

Break-even point = Fixed cost / (Selling price - Unit variable cost) = $100,000 / $(12 - 10) = $100,000 / $2 = 50,000